Strictly Ergodic Models Under Face and Parallelepiped Group Actions
Strictly Ergodic Models Under Face and Parallelepiped Group Actions
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DOI：
10.1007/s40304-017-0102-0
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发表时间：
2017-03
影响因子：
0.9
通讯作者：
Wen Huang;S. Shao;X. Ye
中科院分区：
文献类型：
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作者：
Wen Huang;S. Shao;X. Ye
朱厄特-克里格定理指出，每个遍历系统都有一个严格的遍历拓扑模型。在本文中，我们证明了对于遍历系统，严格遍历模型可能需要更多的性质。例如，对角线下面变换中点的轨道闭合也可能是严格遍历的。作为应用，我们证明了遍历平均沿立方体的逐点收敛，这是由Assani(J anal Math 110：241-269,2010)首先证明的。
The Jewett–Krieger theorem states that each ergodic system has a strictly ergodic topological model. In this article, we show that for an ergodic system one may require more properties on its strictly ergodic model. For example, the orbit closure of points in diagonal under face transforms may be also strictly ergodic. As an application, we show the pointwise convergence of ergodic averages along cubes, which was firstly proved by Assani (J Anal Math 110:241–269, 2010).